Its not required, but adding it wouldn't be wrong, it just might come across a little clunky or unintentional. は does wonders to bring extra special attention to what comes before it. If you did 毎朝は, it means "EVERY morning, ..." providing extra emphasis on the "every morning" portion, whereas 毎朝 on its own is just "oh yeah, by the way, in the mornings, i happen to..." casual.

This rule holds for vague times within Japanese, such as 今日 (きょう - today), 明日 (あした - tomorrow), 今 (いま - now), etc... There's no need for は or に.

If you use an absolute time, a particle is required: 九時 (くじ - 9 o'clock), 四時半 (よじはん - 4:30), etc...

I believe that you can turn an absolute time into a relative time by adding 頃 (ごろ) or 位 (ぐらい/くらい) - 九時ごろ (about 9 o'clock), 九時位 (about 9 o'cock). Once you do this, it no longer requires は or に.